The theory of quantized fields in a curved space-time tells us that an ultraviolet completion of GR must come under the form of higher-order contributions in the scalar objects out of curvature contractions, suppressed by inverse powers of the fundamental quantum (Planck) scale [1]}, [2]}. This yields the natural generalization of \(f(\mathcal {R})\)  gravity by including another contraction of the Ricci tensor, \(\mathcal {Q}=g^{\mu \alpha }g^{\nu \beta }R_{\mu \nu }R_{\alpha \beta }\) , via an arbitrary function of these two invariants, i.e. \(f(\mathcal {R},\mathcal {Q})\) . Therefore, the theory (REF ) is generalized to
\( S=\frac{1}{2\kappa ^2} \int d^4x \sqrt{-g} f(\mathcal {R},\mathcal {Q}) + S_m(g_{\mu \nu },\psi _m)\) 
